coprime elements
41Finitely generated abelian group — In abstract algebra, an abelian group ( G ,+) is called finitely generated if there exist finitely many elements x 1,..., x s in G such that every x in G can be written in the form : x = n 1 x 1 + n 2 x 2 + ... + n s x s with integers n 1,..., n… …
42Sieve of Eratosthenes — Sieve of Eratosthenes: algorithm steps for primes below 121 (including optimization of starting from prime s square). In mathematics, the sieve of Eratosthenes (Greek: κόσκινον Ἐρατοσθένους), one of a number of prime number sieves, is a simple,… …
43Dirichlet's theorem on arithmetic progressions — In number theory, Dirichlet s theorem, also called the Dirichlet prime number theorem, states that for any two positive coprime integers a and d, there are infinitely many primes of the form a + nd, where n ≥ 0. In other… …
44Reflexive relation — In mathematics, a reflexive relation is a binary relation on a set for which every element is related to itself, i.e., a relation on S where x x holds true for every x in S.[1] For example, could be is equal to . Contents 1 Related terms 2… …
45Euclid's lemma — (Greek polytonic|λῆμμα ) is a generalization of Proposition 30 of Book VII of Euclid s Elements . The lemma states that:If a positive integer divides the product of two other positive integers, and the first and second integers are coprime, then… …
46Lens space — A lens space is an example of a topological space, considered in mathematics. The term often refers to a specific class of 3 manifolds, but in general can be defined for higher dimensions.In the 3 manifold case, a picturesque description of a… …
47Rational sieve — In mathematics, the rational sieve is a general algorithm for factoring integers into prime factors. It is essentially a special case of the general number field sieve, and while it is far less efficient than the general algorithm, it is… …
48Kloosterman sum — In mathematics, a Kloosterman sum is a particular kind of exponential sum. Let a , b , m be natural numbers. Then :K(a,b;m)=sum {0leq xleq m 1, gcd(x,m)=1 } e^{2pi i (ax+bx^*)/m},Here x* is the inverse of x modulo m . They are named for the Dutch …
49Finitely-generated abelian group — In abstract algebra, an abelian group (G,+) is called finitely generated if there exist finitely many elements x1,...,xs in G such that every x in G can be written in the form x = n1x1 + n2x2 + ... + nsxs with integers n1,...,ns. In this case, we …
50Localization of a ring — In abstract algebra, localization is a systematic method of adding multiplicative inverses to a ring. Given a ring R and a subset S , one wants to construct some ring R* and ring homomorphism from R to R* , such that the image of S consists of… …
